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I know that protons and electrons do not actually spin, although they have the property of spin.

I was learning about MRI. I was introduced to the idea that you have the spin of the proton in the external magnetic field. Since they are not perfectly aligned, it will cause precession just like in a spin top. I understand how precession occurs in spin tops and bike wheels, but that's dependent on the object actually spinning and having the velocity to change.

If protons don't spin, do they actually precess too? I would imagine not, because that would imply that they're actually spinning. If not actually precessing, then what is this precession?

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  • $\begingroup$ They do. You can even use that for measurements in destruction - free material analysis and medicine : MRT what the protons spin is excited and the decay of the aligned spin precession acid is used $\endgroup$ – planetmaker Dec 14 '20 at 8:50
  • $\begingroup$ There is precession, but you don't need to invoke spinning for that. Weinberg, in Lectures On Quantum Mechanics (2012) treats this using Wigner-Eckart theorem, as far as I remember (sec 5.3) $\endgroup$ – Cryo Dec 14 '20 at 9:16
  • $\begingroup$ @planetmaker so if I had a super microscope, I could SEE them precessing like little spin tops?? $\endgroup$ – John Hon Dec 14 '20 at 9:31
  • $\begingroup$ @JohnHon no. protons are described quantum mechanically, which means all measurable quantities depend on a probability distribution. The probability distribution of many protons in the same boundary conditions will show the precession. $\endgroup$ – anna v Dec 14 '20 at 11:54
  • $\begingroup$ You will get more access to MRI if - only for your imagination - think about the spin together with the electrons magnetic dipole moment. Any external magnetic field will align a bit the electrons dipole and during the relaxation after switched-off external field photons get emitted.MRI is a lot of mathematics to reconstruct from this radiation the 3D picture of the inner structure of a body. $\endgroup$ – HolgerFiedler Dec 20 '20 at 17:51
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Proton and electron spin are like angular momentum in every aspect. It is just that we do not have a mechanical model of a rotating charge to explain it. Electrons and quarks, which give protons their spin, are point particles for all we know donut is hard to think of them as rotating charges.

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Protons and spin of particles of similar dimensions have to be described by quantum mechanical probability distributions which can be predicted using the solutions of the appropriate quantum mechanical equations.

Spin is part of angular momentum at the quantum frame, but neither can be directly observed as one would observe the trajectory of a spinning top. The (x,y,z) of particles in the quantum mechanical frame are described by orbitals , probability loci where a measurement will give the non-sequential (x,y,z) of a particle.

If one could measure a large number of same boundary condition protons, the accumulation of the loci for those protons would show the necessary precession due to angular momentum in the given state, to be checked with quantum mechanical calculations.

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